Problem: $z=77-27.8i$ What are the real and imaginary parts of $z$ ? Choose 1 answer: Choose 1 answer: (Choice A) A $\text{Re}(z)=77$ and $\text{Im}(z)=-27.8i$ (Choice B) B $\text{Re}(z)=-27.8i$ and $\text{Im}(z)=77$ (Choice C) C $\text{Re}(z)=77$ and $\text{Im}(z)=-27.8$ (Choice D) D $\text{Re}(z)=-27.8$ and $\text{Im}(z)=77$
Solution: Background Complex numbers are numbers of the form $z={a}+{b}i$, where $i$ is the imaginary unit and ${a}$ and ${b}$ are real numbers. [What is the imaginary unit?] The real part of $z$ is denoted by $\text{Re}(z)={a}$. The imaginary part of $z$ is denoted by $\text{Im}(z)={b}.$ Finding the Real and Imaginary Parts of $z$ In this case, $z={77}-{27.8}i$ is of the form ${a}+{b}i$, where ${a}={77}$ and ${b}={-27.8}$. Therefore: $\text{Re}(z)={a}={77}$. $\text{Im}(z)={b}={-27.8}$. Summary $\text{Re}(z)={77}$ and $\text{Im}(z)={-27.8}$.